How to make this disappear?

I recently had 3 large ash trees cut down, however one was growing from under my shed and around my old coop. The arborist left a fair stump behind as it had part of the coop’s steel frame in it.

I’ve started to dig around the roots, but very keen to know if there’s an easy way!

I’m looking to extend my shed in the future, so I want the stump largely gone.

Cheers!